WASHINGTON -- The Navy's apology yesterday to the family of the sailor whom officials implicated in the deadly explosion aboard the USS Iowa raised hopes that legal claims may be settled soon and more than two years of anguish brought to an end.

"I'm optimistic, in light of the apology and the Navy's admission ,, that the accusation shouldn't have been made, that the next step should be for us to sit down and discuss this rationally to arrive at a fair settlement," said Kreig J. Brusnahan, attorney for the family of Petty Officer 2nd Class Clayton M. Hartwig, a gunner's mate.

"They are coming to realize the horror they inflicted on this family," he said.

At the Pentagon, the Navy's highest officer reversed an official finding that the blast that killed 47 crewmen on April 19, 1989, "most probably" was triggered by Petty Officer Hartwig, 24, of Cleveland, whom senior Navy investigators called despondent and suicidal.

The Navy had contended that the sailor probably slipped a homemade chemical detonator between powder bags being loaded into the center gun of one of the ship's forward 16-inch gun turrets.

Although the Navy had earlier ruled out an accidental cause for the explosion, Admiral Kelso said that that conclusion could not be supported by the results of an extensive new investigation that the Navy began more than a year ago.

The admiral also announced changes in investigative procedures, including adoption of a higher "clear and convincing" standard of proof when deceased sailors are suspected of deliberate acts. The older standard allowed a conclusion to be drawn on a "preponderance of evidence."

Members of the Hartwig family said they were pleased with the apology, delivered in writing to their Cleveland home by Rear Adm. Douglas J. Katz, the same officer who brought them news of Petty Officer Hartwig's death 2 1/2 years ago.

"It was worded well enough that we accepted it as a full apology," said Earl Hartwig, whose service on a Navy destroyer during World War II inspired his son to join a combat ship. "We know the Navy is saying they'd like to get this behind them."

During the meeting with Admiral Katz, which the family described as relaxed and cordial, "my mother's first question to him was, 'In your heart, is this a sincere apology?' " said Kathy Kubicina, one of Clayton Hartwig's two sisters. "He said it was unequivocal; it was absolute."

Mr. Brusnahan, who also was there, asked Admiral Katz and a Navy lawyer at the meeting to pass a note to Admiral Kelso inviting the Navy to help resolve several outstanding legal claims.

Among the cases stemming from the Iowa explosion is a lawsuit for wrongful death that was filed in U.S. District Court in Alexandria, Va., by attorneys for the Hartwigs and 41 other families. The suit, which claims $2 million for each death, was dismissed last summer but that ruling has been appealed.

The Hartwigs also filed an administrative claim with the Navy in April seeking $40 million in damages for "intentional and negligent infliction of emotional distress." Mr. Brusnahan said that today is the six-month deadline for the Navy to respond and that a federal court suit will be filed if the Navy fails to answer.

Admiral Kelso would not discuss the legal claims, except to say that none of the Navy lawyers he consulted opposed issuing the public apology. "I feel it's the right thing to do," he said.